176 lines
3.3 KiB
Markdown
176 lines
3.3 KiB
Markdown
**Test Yourself**
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Page 73
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1. An _and_ statement is true when, and only when, both components are _______.
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**Solution**
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True.
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2. An _or_ statement is false when, and only when, both components are _______.
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**Solution**
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False.
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3. Two statement forms are logically equivalent when, and only when, they always
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have _______.
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**Solution**
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The same truth values.
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4. De Morgan's laws says (1) that the negation of an _and_ statement is
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logically equivalent to the _______ statement in which each component is
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_______, and (2) that the negation of an _or_ statement is logically
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equivalent to the _______ statement in which each component is _______.
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**Solution**
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or; negated; and; negated.
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5. A tautology is a statement that is always _______.
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**Solution**
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true
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6. A contradiction is a statement that is always _______.
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**Solution**
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false
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---
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**Test Yourself**
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Page 86
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1. An _if-then_ statement is false if, and only if, the hypothesis is _______
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and the conclusion is _______.
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**Solution**
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true; false
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2. The negation of "if $p$ then $q$" is _______.
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**Solution**
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$p$ and not $q$.
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$$ p \wedge \neg q $$
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3. The converse of "if $p$ then $q$" is _______.
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**Solution**
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if $q$ then $p$
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$$ q \to p $$
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4. The contrapositive of "if $p$ then $q$" is _______.
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**Solution**
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if not $q$ then not $p$.
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$$ \neg q \to \neg p $$
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5. The inverse of "if $p$ then $q$" is _______.
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**Solution**
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if not $p$ then not $q$.
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$$ \neg p \to \neg q $$
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6. A conditional statement and its contrapositive are _______.
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**Solution**
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logically equivalent.
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7. A conditional statement and its converse are not _______.
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**Solution**
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logically equivalent.
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8. "$R$ is a sufficient condition for $S$" means "if _______ then _______."
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**Solution**
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$R$; $S$.
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9. "$R$ is a necessary condition for $S$" means "if _______ then _______."
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**Solution**
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$S$; $R$
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10. "$R$ only if $S$" means "if _______ then _______."
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**Solution**
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$R$; $S$
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---
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**Test Yourself**
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Page 99
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1. For an argument to be valid means that every argument of the same form whose
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premises _______ has a _______ conclusion.
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are all true; true
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2. For an argument to be invalid means that there is an argument of the same
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form whose premises _______ and whose conclusion _______.
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are all true; is false
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3. For an argument to be sound means that it is _______ and its premises
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_______. In this case we can be sure that its conclusion _______.
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valid; are all true; is true
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---
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**Test Yourself**
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Page 113
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1. The input/output table for a digital logic circuit is a table that shows
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_______.
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The output signal(s) that correspond to all possible combinations of input
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signals to the circuit.
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2. The Boolean expression that corresponds to a digital logic circuit is
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_______.
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a Boolean expression that represents the input signals as variables and
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indicates the successive actions of the logic gates on the input signals.
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3. A recognizer is a digital logic circuit that _______.
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outputs a 1 for exactly one particular combination of input signals and outputs
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0s for all other combinations.
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4. Two digital logic circuits are equivalent if, and only if, _______.
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they have the same input/output table
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5. A NAND-gate is constructed by placing a _______ gate immediately following an
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_______ gate.
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NOT; AND
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6. A NOR-gate is constructed by placing a _______ gate immediately following an
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_______ gate.
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NOT; OR
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